Zenith, a small metal furniture firm, produces three types of office chairs from steel, aluminum, and leather. The three types of chairs are Baron, Secretary, and Executive. Let X1, X2, and X3 respectively be the optimal number of Baron, Secretary, and Executive chairs to be produced daily. Profit for each Baron chair is $48.0, for each Secretary chair, it is $45.0, and for each Executive chair, it is $40.0. Each chair must pass through the forging and assembly departments. The manager produced the following linear programming formulation for the problem to determine the optimal solution. Input the model in a software (QM for Windows) you downloaded and solve it. Then, using your computer output, answer the questions below.
Maximize (profit,$) Z = 48X1 + 45X2 + 40X3
subject to;
X3 ≥ 10 (market demand) (Constraint 1)
4X1 + 3X2 + 4X3 ≤ 800 (steel, lbs) (Constraint 2)
2X1 + 6X2 + 2X3 ≤ 820 (aluminum, lbs) (Constraint 3)
3X1 + 2X2 + X3 ≤ 580 ( leather, square yards) (Constraint 4)
X1 + 8X2 + 2X3 ≤ 720 (forging, hrs) (Constraint 5)
2X1 + 4X2 + 2X3 ≤ 585 (assembly, hrs) (Constraint 6)
X1,X2,X3 ≥ 0
Input the linear programming formulation above in QM for Windows software you downloaded, and solve it. Save your computer solution output in A file. Using the computer solution output, answer the following questions (a to g), Type out your answers, save as a Word document and submit it together with the saved screen shot of your computer solution output.
B. What is the optimal daily production quantity for each type of chair at Zenith? (That is, how many of each type of chair should Zenith optimally produce daily?) They would be the values of X1, X2, and X3 in the optimal solution.
B. What would Zenith’s optimal daily profit be?
C. Will Zenith use all the available quantities of each of its resources (steel, aluminum, leather, forging hours, and assembly hours) to their limits each day? Be specific for each resource, indicating unused amounts if any.
D. The company can hire additional part-time employee that would increase the hours available in the assembly department by 4 hours daily, at the cost of $5.15 per hour. Should she be hired? Explain.
E. If the profit from each Executive chair increased by $ 5.00, without resolving the new model in the computer, would this change the optimal production quantities? Explain. Give reason for your answer.
F. Zenith's General Manager has been approached by a friend whose company would like to use some hours in the forging department every day. Should Zenith sell some hours to the other firm? If so, how many hours can Zenith sell to this other firm?
G. Suppose that 50 pounds of aluminum supplied on any given day are defective and could not be used, would it change the optimal daily production quantity for each specific type of chair at Zenith? Explain. Give reason for your answer.